POLYOMINO TILINGS

Polyomino Tilings

Select polyominoes for a set (currently 1 or 2), for which tilings should be shown.

Then click "Show" button.

You may also see list of all polyomino sets for which data is available here.


I pentomino and U pentomino

Prime rectangles: ≥ 72.

Smallest rectangle tilings

Smallest rectangle (12x20):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

w \ h
1-9
10
11
12
13
14
15
16
17
18
19
20
N>0
1-9
0
10
0
0
11
0
0
0
12
0
0
0
0
13
0
0
0
0
0
14
0
0
0
0
0
0
15
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
≥1
0
0
0
19
0
0
0
0
0
0
≥1
0
0
0
0
20
0
0
0
40
≥1
≥1
≥1
?
?
?
?
?
21
0
0
0
0
0
0
≥1
0
0
0
0
?
?
22
0
0
0
0
0
0
≥1
0
0
0
0
?
?
23
0
0
0
0
0
0
≥1
0
0
0
0
?
?
24
0
0
0
0
0
0
≥1
0
0
0
0
≥1
?
25
0
0
192
≥586
≥1
≥1
≥1
?
?
?
?
≥1
?
26
0
0
0
0
0
0
≥1
0
0
0
0
≥1
?
27
0
0
0
0
0
0
≥1
0
0
0
0
≥1
?
28
0
0
0
0
0
0
≥1
0
0
0
0
≥1
?
29
0
0
0
0
0
0
≥1
0
0
0
0
≥1
?
30
0
0
≥192
≥586
≥1
≥1
≥1
?
?
≥1
≥1
≥1
?
31
0
0
0
0
0
0
≥1
0
0
0
0
?
?
32
0
0
0
0
0
0
≥1
0
0
0
0
?
?
33
0
0
0
0
0
0
≥1
0
0
0
0
?
?
34
0
0
0
0
0
0
≥1
0
0
0
0
?
?
35
0
0
≥192
≥586
≥1
≥1
≥1
?
?
?
?
?
?
36
0
0
0
0
0
0
≥1
0
0
0
0
≥1
?
37
0
8
0
0
0
0
≥1
0
0
0
0
≥1
?
38
0
16
0
0
0
0
≥1
0
0
0
0
≥1
?
39
0
24
0
0
0
0
≥1
0
0
0
0
≥1
?
40
0
32
≥192
≥1600
≥1
≥1
≥1
?
?
?
?
≥1
?
41
0
52
0
0
0
0
≥1
0
0
0
0
≥1
?
42
0
408
0
0
0
0
≥1
0
0
0
0
≥1
?
43
0
928
0
0
0
0
≥1
0
0
0
0
≥1
?
44
0
1644
0
0
0
0
≥1
0
0
0
0
≥1
?
45
0
2588
≥192
≥23440
≥1
≥1
≥1
?
?
≥1
≥1
≥1
?
46
0
4316
0
0
0
0
≥1
0
0
0
0
≥1
?
47
0
14692
0
0
0
0
≥1
0
0
0
0
≥1
?
48
0
34032
0
0
0
0
≥1
0
0
0
0
≥1
?
49
0
66460
0
0
0
0
≥1
0
0
0
0
≥1
?
50
0
117136
≥36864
≥23440
≥1
≥1
≥1
?
?
?
?
≥1
?
51
0
205384
0
0
0
0
≥1
0
0
0
0
≥1
?
52
0
488032
0
0
0
0
≥1
0
0
0
0
≥1
?
53
0
1072360
0
0
0
0
≥1
0
0
0
0
≥1
?
54
0
2168634
0
0
0
0
≥1
0
0
0
0
≥1
?
55
0
4082864
≥1
≥1
≥1
≥1
≥1
?
?
?
?
≥1
?
56
0
7489910
0
0
0
0
≥1
0
0
0
0
≥1
?
57
0
15459232
0
0
0
0
≥1
0
0
0
0
≥1
?
58
0
31991690
0
0
0
0
≥1
0
0
0
0
≥1
?
59
0
64470720
0
0
0
0
≥1
0
0
0
0
≥1
?
60
0
124953018
≥1
≥1
≥1
≥1
≥1
?
?
≥1
≥1
≥1
?
61
0
236219772
0
0
0
0
≥1
0
0
0
0
≥1
?
62
0
464575494
0
0
0
0
≥1
0
0
0
0
≥1
?
63
0
924549484
0
0
0
0
≥1
0
0
0
0
≥1
?
64
0
1.83377779×10¹⁰
0
0
0
0
≥1
0
0
0
0
≥1
?
65
0
3.57753104×10¹⁰
≥1
≥1
≥1
≥1
≥1
?
?
?
?
≥1
?
66
0
6.86571115×10¹⁰
0
0
0
0
≥1
0
0
0
0
≥1
?
67
0
1.33078071×10¹¹
0
0
0
0
≥1
0
0
0
0
≥1
?
68
0
2.59641574×10¹¹
0
0
0
0
≥1
0
0
0
0
≥1
?
69
0
5.07670953×10¹¹
0
0
0
0
≥1
0
0
0
0
≥1
?
70
0
9.87386156×10¹¹
≥1
≥1
≥1
≥1
≥1
?
?
?
?
≥1
?
71
0
1.90397962×10¹²
0
0
0
0
≥1
0
0
0
0
≥1
?
72
0
3.67406800×10¹²
0
0
0
0
≥1
0
0
0
0
≥1
?
73
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
74
0
≥1
0
0
0
0
≥1
0
0
0
0
≥1
?
N>0
x
all
5k
5k
5k
5k
all
?
?
?
?
?

See Also

I pentomino and T pentominoI pentomino and V pentomino